The existing conventional freight brake system used on railroads in North America for freight cars utilizes a combination "AB" reservoir, having an auxiliary reservoir volume of 2500 cubic inches for service braking and an emergency reservoir volume of 3500 cubic inches for a combined total of 6000 cubic inches for emergency brake applications. The "AB" type control valves, including ABD, ABDW, and ABDX valves, as well as DB-60 control valves, all operate to produce brake cylinder pressure on each car of a train by causing the auxiliary reservoir pressure to be reduced by the same general amount as the train brake pipe pressure is reduced and by directing the air thus released from the reservoir to the brake cylinder. For full service applications, brake pipe pressure is generally reduced by an amount sufficient to allow the auxiliary reservoir pressure to equalize with the brake cylinder pressure, thereby providing the maximum service brake available from a given initial brake pipe pressure. For emergency brake applications, brake pipe pressure is quickly reduced to atmospheric pressure, and both the auxiliary and emergency reservoir pressures equalize with the brake cylinder pressure. This produces a brake cylinder pressure 15% to 20% higher than full service pressure.
The brake cylinder pressure derived for any brake application is therefore somewhat dependent on the initial and final brake cylinder volumes.
Initially, with the brakes unapplied and the brake piston retracted in release position, the brake cylinder piping and clearance volume is at atmospheric pressure (14.7 psi). When the brakes are applied, this initial volume is expanded by the piston displacement volume (piston area multiplied by piston stroke), as the piston is driven out through the brake cylinder. During piston displacement, the forward side of the piston is essentially voided of atmospheric pressure, causing it to behave as a vacuum. Therefore, on a per cubic inch basis, the effect of the volume displaced by the piston has a greater impact on the resultant brake cylinder pressure than does the brake cylinder clearance and piping volume.
In general terms, the clearance and pipe volume for a conventional freight car having a body mounted brake cylinder is approximately 120 cubic inches, and the piston displacement volume is about 630 cubic inches. The initial cylinder volume on the pressure side of the piston is therefore 120 cubic inches, and the final volume is approximately 750 cubic inches.
Knowing the auxiliary reservoir volume and the initial and final brake cylinder volumes, brake cylinder pressure can be calculated, simply using the principles of Boyle's Law.
For service reductions: EQU 2500.multidot.Pi+14.7.multidot.Vc=2500 (Pi-R)+Pc (Vc+Vd) (1)
Where:
Pi=Initial reservoir pressure (psia) PA1 Pc=Brake cylinder pressure (psia) PA1 R=Pressure reduction in brake pipe and reservoir (psi) PA1 Vc=Brake cylinder clearance and piping volume (cubic inches) PA1 Vd=Piston displacement volume (cubic inches) PA1 Pe=Reservoir & Brake Cylinder equalization pressure (psia) PA1 Pem=Emergency brake cylinder pressure (psi) PA1 R is supply reservoir pressure reduction (psi) PA1 Vs=Supply reservoir volume (cubic inches) PA1 Vfe=fixed equalizing reservoir volume (cubic inches)
This can be reduced, as follows: EQU 2500.multidot.R=Pc (Vc+Vd)-14.7.multidot.Vc (2)
Letting Vc=120 cubic inches and Vd=630 cubic inches EQU 2500R=750Pc-1764 (3) EQU Pc=3.33R+2.35 (4) EQU Pc(gage)=3.33R+2.35-14.7 or 3.33R-12.35 (5)
In general, then, gage brake cylinder pressure for a service reduction with conventional brake equipment can be expressed as Pcg=3.33R-12.35, where R is pressure reduction from the auxiliary reservoir.
For full service equalization, the equalization equation can be written as: EQU Pi.multidot.2500+14.7 Vc=Pe (2500+Vc+Vd) (6)
where:
Using the standard volumes, this equation reduces to: EQU 2500.multidot.Pi+1764=3250.multidot.Pe (7) EQU Pe(gage)=0.769 Pi-14.157 (8)
For Emergency applications: EQU Pi.multidot.6000+14.7.multidot.Vc=Pem (6000+Vc+Vd) (9)
and, EQU 6000.multidot.Pi+1764=6750.multidot.Pem (10)
reducing to: EQU Pem(gage)=0.8889Pi-14.439 (11)
where:
Because the conventional system relies directly on the relationship of the reservoir and brake cylinder volumes, the actual brake cylinder pressure on each car can vary as a result of having somewhat different brake cylinder piston strokes and piping arrangements on such cars.
One method of compensating for this condition and obtaining generally equal brake cylinder pressures, irrespective of piston travel or piping volume variations, is by using a fixed equalizing volume and a relay valve to supply the actual brake cylinder pressure. Such systems are hereinafter referred to as relayed systems.
In such a relayed system the control valve output from the reservoirs is fed to a fixed volume equalizing reservoir, not having a moving piston, and the pressure in this equalizing reservoir is used to supply a control pressure to a conventional relay valve. The relay valve simply causes a separate supply reservoir to feed as much air pressure to the brake cylinder as is required for the brake cylinder pressure to match the control pressure, irrespective of the actual volume of the brake cylinder. One such relayed system is shown in FIG. 1 of the drawings.
Conventional pneumatic relay valves are generally proportional, where the output pressure is either equal to or a fixed proportion of the control pressure. With conventional relay valves, however, it is not possible to derive output pressures which match the brake cylinder pressure of the conventional brake system for the full range of service reductions and also service and emergency equalizations. This is due to the fact that the actual brake cylinder has the movable piston that creates a voided displacement volume, whereas the aforementioned fixed equalizing reservoir volume in a relayed system does not have a movable piston.
Graphically, FIG. 2 shows the brake cylinder pressure, Pe, versus reservoir reduction for a fixed equalizing reservoir volume and a characteristic brake cylinder pressure curve, Pc, for a brake cylinder as typically employed in "AB" type brake systems. The 3.7 psi reduction to derive zero (gage) brake cylinder pressure indicates that a pressure reduction of 3.7 psi is required from the 2500 cubic inch auxiliary reservoir to pressurize the voided 630 cubic inch piston displacement volume to atmospheric pressure (14.7 psia, or 0 psig). This corresponds to 12.3 psi buildup in the pressure Pe of a fixed volume equalizing reservoir. With no such displacement volume, the pressure buildup in a fixed volume equalizing reservoir begins at the first incremental reduction above zero reduction. The slope of this line is determined directly by the ratio of the auxiliary reservoir and equalizing reservoir volumes. It can be shown that the general equation for the pressure buildup in a fixed volume equalizing reservoir, when supplied from another pressurized reservoir, is: EQU Pe(gage)=R (Vs/Vfe) (12)
Where:
In a relay valve which utilizes the pressure in a fixed volume equalizing reservoir as a control pressure and feeds air pressure from a supply reservoir to one or more brake cylinders having a movable piston, one element which can be added to allow the output of such a relay to better match the brake cylinder pressure of the described conventional brake system for any given pressure reduction is an offsetting spring.
The load of this spring can be set such that it balances approximately 12.3 psi acting on the effective area of the relay valve control piston when the supply valve is positioned right at its opening point, since the brake cylinder pressure in a conventional system would in essence be 12.3 psi higher for any given reduction if the piston displacement volume were pressurized to atmospheric pressure to begin with.
In its simplest form, such a relay valve, having the 12.3 psi offsetting spring, will generally match the desired brake cylinder pressures for partial service reductions when used in a system where the brake control valve uses an auxiliary reservoir having a volume of 3.33 times the volume of the fixed volume equalizing reservoir.
In such a relayed system, this volumetric ratio matches the nominal ratio of the auxiliary reservoir and final brake cylinder volume of a conventional system, thereby obtaining the proper slope of brake cylinder pressure versus reduction, and the spring in the relay valve shifts the brake cylinder output by 12.3 psi below the equalizing reservoir control pressure Pe to generally match the desired brake cylinder pressure that would be obtained with a conventional system. This offset spring is included in the relay valve of the present invention.
Making the ratio of volumes in a relayed system match the volumetric ratio of the auxiliary reservoir and brake cylinder in a conventional system and utilizing the proper offset spring, however, only assures that the brake cylinder relay valve will provide compatible operation with a conventional brake system on railroad cars during partial service reductions. Without the effect of a voided piston displacement volume consuming a certain amount of reservoir air to charge it to atmospheric pressure, a fixed volume auxiliary reservoir and fixed volume equalizing reservoir will not equalize at the same pressures as the conventional system from any initial pressure, and the described relay valve, even with the offset spring, will therefore not provide proper full service or emergency brake cylinder pressures.